What is the integral of (9x(x^8-1/9)) ?

The integral of (9x(x^8-1/9)) is 9(1/18 x^2(9x^8-1)-(2x^{10})/5)+C

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integral of (9x(x^8-1/9))

\int (9 x (x^{8} - \frac{1}{9})) d x

9 (\frac{1}{18} x^{2} (9 x^{8} - 1) - \frac{2 x ^{10}}{5}) + C

Solution steps

\int 9 x (x^{8} - \frac{1}{9}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int x (x^{8} - \frac{1}{9}) d x

Apply Integration By Parts

: \frac{1}{18} x^{2} (9 x^{8} - 1) - \int 4 x^{9} d x

= 9 (\frac{1}{18} x^{2} (9 x^{8} - 1) - \int 4 x^{9} d x)

\int 4 x^{9} d x = \frac{2 x ^{10}}{5}

= 9 (\frac{1}{18} x^{2} (9 x^{8} - 1) - \frac{2 x ^{10}}{5})

Add a constant to the solution

= 9 (\frac{1}{18} x^{2} (9 x^{8} - 1) - \frac{2 x ^{10}}{5}) + C

\frac{d}{d x} (\frac{tan ( x ) - 4}{sec ( x )})

\frac{d}{d x} (\frac{7}{( x ^{2} - 1 ) ^{3}})

\frac{d}{d x} (- 2 x^{3} - 3 x^{2} + 12 x + 11)

f (x) = 3 x^{2} + 5 x, at x = - 3

\frac{\partial}{\partial x} (e^{- 5 x})

What is the integral of (9x(x^8-1/9)) ?
The integral of (9x(x^8-1/9)) is 9(1/18 x^2(9x^8-1)-(2x^{10})/5)+C